If chlamydia and gonorrhea can be tested by a urine test, then is it possible to contract them through a toilet splash on my genitals?

No: Very very less likely someone will acquire the infection by toilet splash. Usually it requires mucosal surface contact for spread of these bacteria. Thanks

Very Unlikely: The most common toilet related transmission is ring worm and even that is rare. If you have symptoms you need to be seen however.

No: It seems logical that if chlamydia and gonorrhea are in urine then urine could transmit the disease, but transmission from urine splash is so unlikely as to be virtually impossible. Risk of infection has a lot to do with exposure. While urine might have some of the organisms in it, the amount is not likely to be very high, and the viability is not likely to be good.